Thursday 13 October 2016

thermodynamics - What is the meaning of following expression $C=frac{delta Q}{dT}$ mathematically?


Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics):


Many text books (even Wikipedia) writes wrong expressions (from mathematical point of view) for Heat Capacity Coefficient, and the right way to wright it is as following: $$C=\frac{\delta Q}{dT}.$$ But as we see it is neither usual differential, nor a functional derivative, so the question what is this?


I couldn't find the answer in math books, and it is true that many text books writes it in very different ways mixing exact and inexact differentials, so anybody have a clue what is the right expression for c and why from mathematical point of view?




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